Method of determining the time for polishing the surface of an integrated circuit wafer

ABSTRACT

A method of determining the time for polishing the surface of an integrated circuit wafer on a polishing machine. A sample wafer is fabricated to include at least one high plateau and at least one low plateau joined by a sudden transition. At least one initial profile is topographically scanned, and the surface of the sample wafer is polished at a particular polishing pressure for a particular polishing time. The final profile of the polished layer is topographically scanned in the corresponding area, and the initial and final topographical scans of the sample wafer are converted into Fourier series. The surface of the wafer to be polished is topographically scanned, and the topographic scan of the wafer to be polished is converted into a Fourier series. The time for polishing the wafer to be polished is calculated from the Fourier series and the average thickness to be removed.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application is based upon and claims priority from priorFrench Patent Application No. 00-08576, filed Jul. 3, 2000, the entiredisclosure of which is herein incorporated by reference.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The present invention relates to semiconductor devicefabrication, and more specifically to the polishing of the surface of anintegrated circuit wafer.

[0004] 2. Description of Related Art

[0005] The present invention is directed to a method of determining thetime for polishing the surface of an integrated circuit wafer, whichincludes a layer of a material to be polished, on a mechanical/chemicalpolishing machine. Conventionally, the polishing time for the surface ofa wafer is determined through trial and error on successive wafers. Thistrial and error process causes the successive wafers that are used tomake the polishing time determination to then be unusable, so they mustconsequently be rejected.

SUMMARY OF THE INVENTION

[0006] In view of these drawbacks, it is an object of the presentinvention to overcome the above-mentioned drawbacks and to provide amethod for determining the time for polishing an integrated circuitwafer so as to remove from a layer to be polished a predeterminedaverage thickness so as to confer on it a particular final topography.

[0007] One embodiment of the present invention provides a method ofdetermining the time for polishing the surface of an integrated circuitwafer to be polished on a polishing machine so as to remove from a layerof a material to be polished a predetermined average thickness andconfer a particular final topography. According to the method, a samplewafer is fabricated by depositing a layer of the material to be polishedsuch that the layer forms at least one high plateau and at least one lowplateau that are joined by a sudden transition. At least one initialprofile of the layer that includes the transition on the surface of thesample wafer is topographically scanned, and the surface of the samplewafer is polished on the polishing machine at a particular polishingpressure for a particular polishing time. The final profile of thepolished layer is topographically scanned in an area corresponding tothe initial profile, and the initial topographical scan and the finaltopographical scan of the sample wafer are converted into Fourierseries. The surface of the wafer to be polished is topographicallyscanned, and the topographical scan of the wafer to be polished isconverted into a Fourier series. The time for polishing the wafer to bepolished is calculated from the Fourier series and the average thicknessto be removed. In a preferred embodiment, the wafer to be polished ispolished for the calculated polishing time.

[0008] Other objects, features, and advantages of the present inventionwill become apparent from the following detailed description. It shouldbe understood, however, that the detailed description and specificexamples, while indicating preferred embodiments of the presentinvention, are given by way of illustration only and variousmodifications may naturally be performed without deviating from thepresent invention.

BRIEF DESCRIPTION OF THE DRAWINGS

[0009]FIG. 1 is a diagram of an exemplary polishing machine;

[0010]FIG. 2 is a plan view of a sample wafer;

[0011]FIG. 3 shows a part of the sample wafer of FIG. 2 incross-section;

[0012]FIG. 4 is a plan view of a wafer to be polished; and

[0013]FIG. 5 shows a part of the wafer of FIG. 4 in cross-section.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

[0014] Preferred embodiments of the present invention will be describedin detail hereinbelow with reference to the attached drawings.

[0015] Preferred embodiments of the present invention provide methodsfor determining the time for polishing an integrated circuit wafer (suchas one of a series of identical wafers to be polished in the same way)so as to remove from a layer to be polished (such as a layer ofdielectric material) a predetermined average thickness so as to conferon it a particular final topography. In preferred embodiments of thepresent invention, the wafer or wafers to be polished are regarded ashaving particular constructional and adjustment characteristics, inparticular on a polishing machine in which the wafer to be polished isgripped at a particular pressure (Po) between a rotary head and apolishing cloth carried by a turntable and covered with an abrasivematerial.

[0016] In one preferred embodiment, a sample wafer is fabricated bydepositing a layer of the material to be polished so that the layerforms at least one high plateau and one low plateau that are joined by asudden transition, and at least one initial profile of the layer thatincludes the transition is topographically scanned. Then, the surface ofthe sample wafer is polished on the polishing machine at a particularpolishing pressure (Po) and for a particular polishing time (t). Next,the final profile of the layer polished in this way is topographicallyscanned in the area corresponding to the initial profile. The initialtopographical scan and the final topographical scan of the sample waferare converted into Fourier series.

[0017] Additionally, the surface of the wafer to be polished istopographically scanned and the topographic scan of the wafer to bepolished is converted into a Fourier series. Then, the time (T) forpolishing the wafer to be polished is calculated from the Fourier seriesand the average thickness (e_(m)) to be removed. Once that time isknown, the wafer or series of wafers to be polished are each polishedfor the polishing time (T) so that the final topography of the surfaceof the polished wafer corresponds to the required topography.

[0018] One embodiment of the present invention will now be explained indetail with reference to FIGS. 1-5. FIG. 1 shows an exemplarymechanical/chemical polishing machine. As shown, the mechanical/chemicalpolishing machine 1 conventionally includes a turntable 2 covered with apolishing cloth 3, a rotary polishing head 4, and a nozzle 5 for feedingan abrasive material onto the polishing cloth 3. A wafer 6 to bepolished is gripped between the rotary head 4 and the turntable 2 sothat its face 7 to be polished is in contact with the polishing cloth 3.

[0019] The polishing machine 1 therefore has particular structural,functional, and adjustment characteristics, including in particular therotation speeds of the head 4 and the turntable 2, the particularmechanical properties of the polishing cloth 3, the materialconstituting the abrasive fed via the nozzle 5, and a particularpolishing pressure Po. Accordingly, the thickness or average thicknessremoved from the wafer 6, and therefore the final topography of thesurface of the wafer 6 after polishing, depend on the time during whichthe wafer is polished on the machine 1.

[0020] The method used to determine the time for polishing an integratedcircuit wafer 8 shown in FIGS. 4 and 5 will now be described. The wafer8 includes a multiplicity of identical areas 9 corresponding tointegrated circuits to be fabricated. The surface of the wafer 8 hasprojecting and recessed parts and includes a dielectric material layer10 which espouses the shapes of identical underlying patterns, forexample metal patterns, in each area 9.

[0021] First Step

[0022] A sample wafer 11 shown in FIGS. 2 and 3 is first fabricated andincludes a multiplicity of regularly distributed parallelepiped-shapedpatterns 12 (for example, made of a metal). The surface of the samplewafer 11 is covered with a layer 13 of a material identical to that ofthe layer 10 of the wafer 8 to be polished (for example, a dielectricmaterial). The layer 13 therefore includes high plateaux 14 and lowplateaux 15, which are joined by abrupt transitions 16. The highplateaux 14 are above the patterns 12, and the surface of the samplewafer resembles a chessboard. In one exemplary embodiment, the squaresconstituting the chessboard have a side length of 18 millimeters and thedifference in altitude between the high plateaux and the low plateaux isequal to one micron.

[0023] An initial profile 17 of the layer including a transition 16 onthe surface of the sample wafer 11 is then scanned topographically (forexample, by optical measurements, using conventional reflectometry andprofilometry apparatus) at different points of an abscissa line 18 whichis perpendicular to a transition 16 and on respective opposite sides ofthat transition on the low plateau 14 and on the high plateau 15, toconstitute an initial matrix Me(initial) associating the abscissae xwith the corresponding altitudes v(x,0). In one exemplary embodiment,200 points distributed over a distance of 9 millimeters to either sideof the transition 16 are scanned.

[0024] Second Step

[0025] The sample wafer 11 is then placed on the machine 1 and itssurface is polished at a particular polishing pressure Po for apolishing time t. A final profile 19 on the surface of the sample wafer11 is then scanned topographically (for example, by optical measurementsusing conventional reflectometry and profilometry apparatus) atdifferent points of the aforementioned abscissa line 17, to constitute afinal matrix Me(final) associating the abscissae x with thecorresponding altitudes v(x,t).

[0026] Third Step

[0027] The initial matrix Me(initial) and the final matrix Me(final) arestored in a programmed computer along with operating conditions of thepolishing machine 1, such as the polishing pressure Po, the attack speedVa, and the time t for which the sample wafer is polished. The scannedmatrices are then converted into Fourier series by applying thefollowing two equations. $\begin{matrix}{{{{v\left( {x,0} \right)} = {\sum\limits_{i}{{A_{i}(0)} \cdot {\cos \left( \frac{2\quad {\pi \cdot x}}{\lambda_{i}} \right)}}}}{and}}} & (I) \\{{v\left( {x,t} \right)} = {\sum\limits_{i}{{A_{i}(t)} \cdot {\cos \left( \frac{2\quad {\pi \cdot x}}{\lambda_{i}} \right)}}}} & ({II})\end{matrix}$

[0028] In the above equations, λ_(i) represents the wavelengths of theFourier series and Ai represents the amplitudes of the components of theFourier series describing the aforementioned profiles.

[0029] Having prefixed at least two particular wavelengths λ₁ and λ₂,the computer then calculates for those particular wavelengths theamplitudes A1(o) and A2(o) of the components of the Fourier seriescorresponding to the initial profile 17 of the sample wafer 11 and theamplitudes A1(t) and A2(t) of the components of the Fourier seriescorresponding to the final profile 18 of the sample wafer 11. In oneexemplary embodiment, those wavelengths are equal to 1 millimeter and 10millimeters.

[0030] Fourth Step

[0031] The fourth step calculates the values of two functionalcoefficients k and D. These coefficients are advantageouslyrepresentative of local deformations of the polishing cloth 3 installedon the polishing machine 1 caused by the polishing operation.

[0032] The computer is programmed to use the following system of twoequations in two unknowns k and D. $\begin{matrix}{{{\frac{A_{1}(t)}{A_{1}(0)} = {\exp \left\lbrack {{- \left( {k + {D \cdot \left( \frac{2\quad \pi}{\lambda_{1}} \right)^{4}}} \right)} \cdot a} \right\rbrack}}{and}}\quad } & ({IIIa}) \\{\frac{A_{2}(t)}{A_{2}(0)} = {\exp \left\lbrack {{- \left( {k + {D \cdot \left( \frac{2\quad \pi}{\lambda_{2}} \right)^{4}}} \right)} \cdot a} \right\rbrack}} & ({IIIb})\end{matrix}$

[0033] In the above equations, “a” is equal to the average thicknesse_(m) removed from the sample wafer 11 divided by the polishing pressurePo, with the average thickness e_(m) removed being equal to the speed ofattack Va multiplied by the time t for which the sample wafer 11 ispolished.

[0034] The computer solves the above system of equations and suppliesthe values of the coefficients k and D. In one exemplary embodiment, thethickness e_(m) is equal to 0.7 microns and the pressure Po is equal to3×10⁴ Pa. Under the above conditions, the coefficient k calculated isequal to 10⁶ Pa.mm⁻¹ and the coefficient D calculated is equal to3.9×10⁷ Pa.mm³.

[0035] Fifth Step

[0036] Having calculated the functional coefficients k and D associatedwith the polishing machine 1, the next step is to calculate the time (T)for polishing the wafer or a series of identical wafers 8 to be polishedon the polishing machine 1. For this purpose, the surface of the wafer 8to be polished is scanned topographically in two orthogonal directions xand y to constitute an initial 3D matrix Mp(initial 3D). The computerthen converts that matrix representing the initial surface of the wafer8 to be polished into a Fourier series by applying the followingequation. $\begin{matrix}{{v\left( {x,y,0} \right)} = {\sum\limits_{i}{\sum\limits_{j}{{A_{i}(0)}{{A_{j}(0)} \cdot {\cos \left( \frac{2{\pi \cdot x}}{\lambda_{i}} \right)} \cdot {\cos \left( \frac{2{\pi \cdot y}}{\lambda_{j}} \right)}}}}}} & ({IV})\end{matrix}$

[0037] In the above equation, x and y are the two directions in whichthe wafer 8 to be polished is scanned. Ai(o) and Aj(o) are theamplitudes of the components associated with the wavelengths λ_(i) andλ_(j) in the directions x and y on the wafer 8 to be polished.

[0038] The computer solves the above equation and delivers the values ofthe components Ai(o) and Aj(o). The computer is programmed to insert theabove values in the following equations, to complete the simulated finaltopography of the surface of the wafer 8 after polishing.$\begin{matrix}{{v\left( {x,y,T} \right)} = {\sum\limits_{i,j}{{A_{i}(0)}{A_{j}(0)}{\exp \left\lbrack {{- \left( {k + {{D\left( {2\quad \pi} \right)}^{4} \cdot \left( {\frac{1}{\lambda_{i}^{2}} + \frac{1}{\lambda_{j}^{2}}} \right)^{2}}} \right)} \cdot \frac{V\quad {a \cdot T}}{P_{0}}} \right\rbrack}{\cos \left( \frac{2\quad \pi \quad x}{\lambda_{i}} \right)}{\cos \left( \frac{2\quad \pi \quad y}{\lambda_{j}} \right)}}}} & (V)\end{matrix}$

[0039] The parameters in the above equation are defined or indicatedabove. The computer then calculates the time T to polish the wafer 8 tobe polished such that the required final topography of the wafer 8 isobtained after that polishing time on the polishing machine 1. The timeT being calculated, all that remains is to program the control system ofthe polishing machine 1 so that each wafer 8 to be polished, installedbetween the polishing cloth 3 and the polishing head 4, is polished fora time period equal to the calculated value T. The other operatingconditions of the machine 1 used to carry out the aforementionedpolishing operation on the sample wafer 11 remain unchanged.

[0040] While there has been illustrated and described what are presentlyconsidered to be the preferred embodiments of the present invention, itwill be understood by those skilled in the art that various othermodifications maybe made, and equivalents maybe substituted, withoutdeparting from the true scope of the present invention. Additionally,many modifications may be made to adapt a particular situation to theteachings of the present invention without departing from the centralinventive concept described herein. Furthermore, an embodiment of thepresent invention may not include all of the features described above.Therefore, it is intended that the present invention not be limited tothe particular embodiments disclosed, but that the invention include allembodiments falling within the scope of the appended claims.

What is claimed is:
 1. A method of determining the time for polishingthe surface of an integrated circuit wafer to be polished on a polishingmachine so as to remove from a layer of a material to be polished apredetermined average thickness and confer a particular finaltopography, the wafer to be polished being gripped by the polishingmachine at a particular pressure between a rotary head and a polishingcloth carried by a turntable and covered with an abrasive material, saidmethod comprising the steps of: fabricating a sample wafer by depositinga layer of the material to be polished such that the layer forms atleast one high plateau and at least one low plateau that are joined by asudden transition; topographically scanning at least one initial profileof the layer that includes the transition on the surface of the samplewafer; polishing the surface of the sample wafer on the polishingmachine at a particular polishing pressure for a particular polishingtime; topographically scanning the final profile of the polished layerin an area corresponding to the initial profile; converting the initialtopographical scan and the final topographical scan of the sample waferinto Fourier series; topographically scanning the surface of the waferto be polished; converting the topographical scan of the wafer to bepolished into a Fourier series; and calculating the time for polishingthe wafer to be polished from the Fourier series and the averagethickness to be removed.
 2. The method according to claim 1, wherein inthe step of converting the initial topographical scan and the finaltopographical scan, the initial topographical scan and the finaltopographical scan of the sample wafer are converted into Fourier seriesby applying the following equations: $\begin{matrix}{{{{v\left( {x,0} \right)} = {\sum\limits_{i}{{A_{i}(0)} \cdot {\cos \left( \frac{2\quad {\pi \cdot x}}{\lambda_{i}} \right)}}}}{and}}} & (I) \\{{v\left( {x,t} \right)} = {\sum\limits_{i}{{A_{i}(t)} \cdot {\cos \left( \frac{2\quad {\pi \cdot x}}{\lambda_{i}} \right)}}}} & ({II})\end{matrix}$

with x and v representing the abscissa and the altitude of points of thescanned profiles, λ_(i) representing wavelengths of the Fourier seriesdescribing the aforementioned profiles, and Ai representing theamplitudes of the components of the Fourier series describing theaforementioned profiles.
 3. The method according to claim 2, furthercomprising the step of calculating for at least two particularwavelengths (λ1,λ2) the amplitudes A1(o) and A2(o) of the components ofthe Fourier series corresponding to the initial profile of the samplewafer and the amplitudes A1(t) and A2(t) of the components of theFourier series corresponding to the final profile of the sample wafer.4. The method according to claim 3, further comprising the step ofcalculating adjustment coefficients k and D by solving the followingsystem of equations: $\begin{matrix}{{{\frac{A_{1}(t)}{A_{1}(0)} = {\exp \left\lbrack {{- \left( {k + {D \cdot \left( \frac{2\quad \pi}{\lambda_{1}} \right)^{4}}} \right)} \cdot a} \right\rbrack}}{and}}} & ({IIIa}) \\{\frac{A_{2}(t)}{A_{2}(0)} = {\exp \left\lbrack {{- \left( {k + {D \cdot \left( \frac{2\quad \pi}{\lambda_{2}} \right)^{4}}} \right)} \cdot a} \right\rbrack}} & ({IIIb})\end{matrix}$


5. The method according to claim 4, further comprising the step ofdecomposing the initial surface of the wafer to be polished into Fourierseries by applying the following equation: $\begin{matrix}{{v\left( {x,y,0} \right)} = {\sum\limits_{i}{\sum\limits_{j}{{A_{i}(0)}{{A_{j}(0)} \cdot {\cos \left( \frac{2{\pi \cdot x}}{\lambda_{i}} \right)} \cdot {\cos \left( \frac{2{\pi \cdot y}}{\lambda_{j}} \right)}}}}}} & ({IV})\end{matrix}$

with x and y representing two directions in which the scans areeffected, and Ai(o) and Aj(o) being the amplitudes of the componentsassociated with the wavelengths λ_(i) and λ_(j) in the directions x andy.
 6. The method according to claim 5, wherein in the step ofcalculating the time for polishing, the time (T) for polishing the waferto be polished is calculated from the following equation:$\begin{matrix}{{v\left( {x,y,T} \right)} = {\sum\limits_{i,j}{{A_{i}(0)}{A_{j}(0)}{\exp \left\lbrack {{- \left( {k + {{D\left( {2\quad \pi} \right)}^{4} \cdot \left( {\frac{1}{\lambda_{i}^{2}} + \frac{1}{\lambda_{j}^{2}}} \right)^{2}}} \right)} \cdot \frac{V\quad {a \cdot T}}{P_{0}}} \right\rbrack}{\cos \left( \frac{2\quad \pi \quad x}{\lambda_{i}} \right)}{\cos \left( \frac{2\quad \pi \quad y}{\lambda_{j}} \right)}}}} & (V)\end{matrix}$


7. The method according to claim 6, further comprising the step ofpolishing the wafer to be polished for the calculated polishing time. 8.The method according to claim 1, further comprising the step ofpolishing the wafer to be polished for the calculated polishing time. 9.A machine-readable medium encoded with a program for determining thetime for polishing the surface of an integrated circuit wafer to bepolished on a polishing machine so as to remove from a layer of amaterial to be polished a predetermined average thickness and confer aparticular final topography, the wafer to be polished being gripped bythe polishing machine at a particular pressure between a rotary head anda polishing cloth carried by a turntable and covered with an abrasivematerial, said program containing instructions for performing the stepsof: fabricating a sample wafer by depositing a layer of the material tobe polished such that the layer forms at least one high plateau and atleast one low plateau that are joined by a sudden transition;topographically scanning at least one initial profile of the layer thatincludes the transition on the surface of the sample wafer; polishingthe surface of the sample wafer on the polishing machine at a particularpolishing pressure for a particular polishing time; topographicallyscanning the final profile of the polished layer in an areacorresponding to the initial profile; converting the initialtopographical scan and the final topographical scan of the sample waferinto Fourier series; topographically scanning the surface of the waferto be polished; converting the topographical scan of the wafer to bepolished into a Fourier series; and calculating the time for polishingthe wafer to be polished from the Fourier series and the averagethickness to be removed.
 10. The machine-readable medium according toclaim 9, wherein in the step of converting the initial topographicalscan and the final topographical scan, the initial topographical scanand the final topographical scan of the sample wafer are converted intoFourier series by applying the following equations: $\begin{matrix}{{{{v\left( {x,0} \right)} = {\sum\limits_{i}{{A_{i}(0)} \cdot {\cos \left( \frac{2\quad {\pi \cdot x}}{\lambda_{i}} \right)}}}}{and}}} & (I) \\{{v\left( {x,t} \right)} = {\sum\limits_{i}{{A_{i}(t)} \cdot {\cos \left( \frac{2\quad {\pi \cdot x}}{\lambda_{i}} \right)}}}} & ({II})\end{matrix}$

with x and v representing the abscissa and the altitude of points of thescanned profiles, λ_(i) representing wavelengths of the Fourier seriesdescribing the aforementioned profiles, and Ai representing theamplitudes of the components of the Fourier series describing theaforementioned profiles.
 11. The machine-readable medium according toclaim 10, wherein said program further contains instructions forperforming the step of calculating for at least two particularwavelengths (λ1,λ2) the amplitudes A1(o) and A2(o) of the components ofthe Fourier series corresponding to the initial profile of the samplewafer and the amplitudes A1(t) and A2(t) of the components of theFourier series corresponding to the final profile of the sample wafer.12. The machine-readable medium according to claim 11, wherein saidprogram further contains instructions for performing the step ofcalculating adjustment coefficients k and D by solving the followingsystem of equations: $\begin{matrix}{{{\frac{A_{1}(t)}{A_{1}(0)} = {\exp \left\lbrack {{- \left( {k + {D \cdot \left( \frac{2\quad \pi}{\lambda_{1}} \right)^{4}}} \right)} \cdot a} \right\rbrack}}{and}}} & ({IIIa}) \\{\frac{A_{2}(t)}{A_{2}(0)} = {\exp \left\lbrack {{- \left( {k + {D \cdot \left( \frac{2\quad \pi}{\lambda_{2}} \right)^{4}}} \right)} \cdot a} \right\rbrack}} & ({IIIb})\end{matrix}$


13. The machine-readable medium according to claim 12, wherein saidprogram further contains instructions for performing the step ofdecomposing the initial surface of the wafer to be polished into Fourierseries by applying the following equation: $\begin{matrix}{{v\left( {x,y,0} \right)} = {\sum\limits_{i}{\sum\limits_{j}{{A_{i}(0)}{{A_{j}(0)} \cdot {\cos \left( \frac{2{\pi \cdot x}}{\lambda_{i}} \right)} \cdot {\cos \left( \frac{2{\pi \cdot y}}{\lambda \quad j} \right)}}}}}} & ({IV})\end{matrix}$

with x and y representing two directions in which the scans areaffected, and Ai(o) and Aj(o) being the amplitudes of the componentsassociated with the wavelengths λ_(i) and λ_(j) in the directions x andy.
 14. The machine-readable medium according to claim 13, wherein in thestep of calculating the time for polishing, the time (T) for polishingthe wafer to be polished is calculated from the following equation:$\begin{matrix}{{{v\left( {x,y,T} \right)} = {\sum\limits_{i\quad j}{{A_{i}(0)}{A_{j}(\quad 0)}\quad {\exp\left\lbrack \quad {{- \left( {k + {{D\left( {2\quad \pi} \right)}^{4} \cdot \left( {\frac{1}{\lambda_{i}^{2}} + \frac{1}{\lambda_{j}^{2}}} \right)^{2}}} \right)} \cdot \frac{V\quad {a \cdot T}}{P_{0}}} \right\rbrack}\quad {\cos\left( \quad \frac{2\quad \pi \quad x}{\lambda_{i}} \right)}\quad {\cos \left( \frac{2\quad \pi \quad y}{\lambda_{j}} \right)}}}}\quad} & (V)\end{matrix}$


15. The machine-readable medium according to claim 14, wherein saidprogram further contains instructions for performing the step ofpolishing the wafer to be polished for the calculated polishing time.16. The machine-readable medium according to claim 9, wherein saidprogram further contains instructions for performing the step ofpolishing the wafer to be polished for the calculated polishing time.